The remarkable discovery of cosmic acceleration poses two fundamental questions. (1) Does acceleration reflect the presence of a new energy component or the breakdown of General Relativity on cosmological scales? (2) If acceleration is caused by a new energy component, is it constant in space and time as expected for fundamental vacuum energy, or does it show evolution or variation that imply a dynamical field? After briefly reviewing some of the theoretical ideas for explaining cosmic acceleration, I will turn to observational methods for addressing these questions, with emphasis on recent results from baryon acoustic oscillations (BAO), weak gravitational lensing, and measurements of the Hubble constant, and plans for future facilities such as the Dark Energy Spectroscopic Instrument (DESI), the Euclid mission, the Large Synoptic Survey Telescope (LSST), and NASA's Wide Field Infrared Survey Telescope (WFIRST).